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of pure inductors and capacitors: (a) (b) 10. 3 series and parallel resonance L1 L3 C2 L1 C2 C3 Quantitative analysis: (a) 1)( j 1 jj1j)j1(jj)(2123123132121321213??????????????????CLωLLωCLLωCLωLωLωCωLωCωLωLωZ?When Z(? )=0, numerator is zero: 0)( 31223132 ??? LLωCLLωL1 L3 C2 The following results can be derived: i t ) ( d i s c a r d 02 ?ωr e s o n a n ce ) ( s e r i e s 231312 CLLLLω ??When Y(? )=0, denominator is zero: 012121 ??CLωr e s o n a n c e ) ( p a r a l l e l 1211 CLω ? ? 1? 2 L1 L3 C2 21 ωω ?)1()(1j1 j j1j1 jj1 j j1)(2123321221213212131CLωωCCCLωCLωωLωCωCωLωCωLωCωZ????????????(b) Let numerator and denominator be zero respectively: series resonance )(13211 CCLω ??parallel resonance 2121CLω ?L1 C2 C3 Frequency response of impedance: ? 1 ? X(? ) O ? 2 Z (? )=jX(? ) ? 1 ? X(? ) O ? 2 (a) (b) Ex: The source u1(t) includes two parts of different frequencies ? ?2 (?1?2): Find the way to make u2(t) only include the ?1 part. u1(t) =u11(?1)+u12(?2) Application of LC series and parallel circuit: 1. various types of passive filters + _ u1(t) u2(t) Various types of filter circuits: L2 L1 C2 L3 C1 C3 L2 L1 C2 C1 L3 C3 bandpass filter band stop filter